Question

100 points!!!!!!!

please help!! quadratic word problem. have already posted this for 50 points and someone only said "answering for points" i really need help tho!! its due at midnight tonight and my parents take electronics at 830!!

Answer 1

The minimum unit cost is equal to $15,339

Explanation:

Let

x ----> the number of engines

C ---> the cost in dollars to make each airplane engine

we have

`C(x)=0.5x^(2) -100x+20,339`

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex represent the minimum of the parabola

The minimum unit cost is equal to the y-coordinate of the vertex

Convert the quadratic equation into vertex form

Factor 0.5

`C(x)=0.5(x^(2) -200x)+20,339`

Complete the square. Remember to balance the equation by adding the same constants to each side

`C(x)=0.5(x^(2) -200x+100^2)+20,339-5,000`

`C(x)=0.5(x^(2) -200x+10,000)+15,339`

Rewrite as perfect squares

`C(x)=0.5(x-100)^(2)+15,339` ----> equation into vertex form

The vertex is the point (100,15,339)

The y-coordinate of the vertex is 15,339

therefore

The minimum unit cost is equal to $15,339